Ordinal notations based on a hierarchy of inaccessible cardinals (Q1109768)
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scientific article; zbMATH DE number 4070890
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ordinal notations based on a hierarchy of inaccessible cardinals |
scientific article; zbMATH DE number 4070890 |
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Ordinal notations based on a hierarchy of inaccessible cardinals (English)
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1987
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The author generalizes results on notation systems of \textit{K. Schütte} [Proof theory (1977; Zbl 0367.02012)] and \textit{W. Buchholz} [Lect. Notes Math. 500, 4-25 (1975; Zbl 0342.02021)], and obtains, via so-called Skolem hulls and 2-place functions from the ordinals into the inaccessible cardinals, a new ordinal notation system. This research was motivated by the fact that \((\Delta^ 1_ 2-CA)+BI\) has a model at the first recursively inaccessible ordinal in the constructible hierarchy.
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Skolem hulls
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inaccessible cardinals
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ordinal notation system
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recursively inaccessible ordinal
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constructible hierarchy
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0.9121573
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0.8914901
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0.8867921
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0.8844275
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0.8767462
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0.8737059
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0.87351155
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0.8708359
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